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Compactness of derivations from commutative Banach algebras

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Heath M.

Banach Center Publications

2010

tom 91

nr 1

191-198

We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give an example (due to J. F. Feinstein) of a non-compact, bounded derivation from a uniform algebra A into a symmetric A-bimodule.

Ograniczanie wyników

1 Banach Center Publications

1 Heath M.

1 2010

Wyniki wyszukiwania

Compactness of derivations from commutative Banach algebras